6.EE.A.4 Tutor Intake -- Identifying Equivalent Expressions

They give the same result for at least one value of the variable.

They give the same result for every value substituted for the variable.

They look the same when written out.

They both use the same variable letter.

Testing only one value is against the rules, even if it works.

Two values are needed because expressions always have exactly two terms.

A single match could be a coincidence; a mismatch at a second value would disprove equivalence.

One test is enough, but two values make the answer look more official.

No — testing $x = 1$ gives $8$ for the first expression and $18$ for the second, so they are not equivalent.

Yes — since they use the same numbers and the same variable, they must be equivalent.

Yes — both expressions simplify to the same value for any $x$ because they contain identical parts.

No — they cannot be equivalent because one expression uses parentheses and the other does not.

The expressions might be equivalent — try more values before deciding.

The student made an arithmetic error, since equivalent-looking expressions should always match.

The result is inconclusive — a single test can never determine equivalence either way.

The expressions are not equivalent — the mismatch at $c = 1$ is a counterexample, and one mismatch is enough to settle the question.

$4(2y + 12)$

$4(2y + 3)$

$8(y + 12)$

$4y + 3$